Incorrect test answers for an English test? (Urgent!)

I want to preface this and say that I am not a native English speaker. I’m planning to get into the university and to do it, I have to take a test to show how good my English is. And in this test several questions left me wondering why my answer got marked as incorrect. Here are these questions and the answer options:

Which of the two manuals is … ? I think … ; … is not up to date.

1. the most useful … the big one; the small
2. the most useful one … the bigger; the smaller one (my answer)
3. the more useful … the big one; the smaller
4. many more useful … the biggest; the small

It’s incredible! I … to pay the rent.

1. ,who had no any income, will have
2. ,who have no income at all, will have
3. ,who has no income at all, will have (my answer)
4. have had no income at all than, that’s why I had

The first question is a bit weird and, frankly, I don’t like any options here but I like the part "the smaller one is not up to date" in my answer because of the word "one". From my perspective, "the small(er) is not up to date" sounds clunky because "the small(er)" acts as a nominalized adjective but without "one" it seems like it’s lacking something. Maybe I’m wrong.

The second one also caught me off-guard when I saw it. I guess the test creators expected me to answer ", who have no income…" but the third option sounded more natural to my ears. I have looked up online that there’s a huge debate about it and more conservative English grammarians would probably put "have" here, not "has". But I just wonder if "has" can be considered more informal, but still correct English?

Any help with these questions is appreciated!